SOLUTION: what is (x^1/2 -1/4x^-1/2 ) ^2....

Algebra ->  Distributive-associative-commutative-properties -> SOLUTION: what is (x^1/2 -1/4x^-1/2 ) ^2....      Log On


   

Question 186820: what is (x^1/2 -1/4x^-1/2 ) ^2....
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28x%5E%281%2F2%29+-%281%2F4%29x%5E%28-1%2F2%29+%29+%5E2 Start with the given expression.


%28x%5E%281%2F2%29+-%281%2F4%29%2F%28x%5E%281%2F2%29%29+%29+%5E2 Rewrite x%5E%28-1%2F2%29 as 1%2Fx%5E%281%2F2%29


%28sqrt%28x%29+-%281%2F4%29%2F%28sqrt%28x%29%29%29+%29+%5E2 Convert to radical notation


%28sqrt%28x%29+-+1%2F%284%2Asqrt%28x%29%29+%29+%5E2 Multiply and simplify


FOIL



Multiply


Square the square roots to eliminate them


x-1%2F4-1%2F4%2B1%2F%2816x%29 Multiply


x-1%2F2%2B1%2F%2816x%29 Combine like terms.


So %28x%5E%281%2F2%29+-%281%2F4%29x%5E%28-1%2F2%29+%29%5E2=x-1%2F2%2B1%2F%2816x%29